The Education Minister Jan O'Sullivan is insisting she will not "completely capitulate" on plans for Junior Certificate reform.
It comes as secondary school teachers prepare for more action over the plans, with a lunchtime protest planned for the end of this month.
An independent chairman drew up proposals to try and resolve the dispute earlier this year, but these were rejected by some teachers.
Ms O'Sullivan says she will push ahead with the reforms, despite teachers refusal to grade their own students.
The ASTI is holding its conference in Killarney amid deepening division over reforms of the Junior Cert cycle.
Ms O'Sullivan is addressing one of the secondary teachers unions, the TUI, today.
She told the Pat Kenny Show here on Newstalk there has to be give and take.
Pat King, General-Secretary of the ASTI, says the union will not back down - but it is still hoping to engage with the minister over the Junior Cert.
However, at the beginning of last month, Mr King spoke to Lunchtime and stated that the minister had not been snubbed but that the lack of invitation was simply because of a lack of decision on the matter by the executive.
He said: "There was a discussion in January as to who we invite and there was a deferral of the decision about inviting the Minister. We were extremely busy with the dispute over the Junior Cycle which is ongoing."
"The issue of inviting the minister wasn't revisited by our Executive so the Minister hasn't been invited to the conference."
Speaking to Lunchtime, Ed Walsh, Founding President of University of Limerick, discussed the issue of pay which has been raised at these conferences.
"I suppose Teacher Unions in all countries are there to improve their pay and conditions as best they can but strangely in Ireland because of the veto teachers exercise over government because they control state examinations, they have managed to find their way into all sorts of areas which have been excluded elsewhere.
"I'm not aware of teachers living in abject poverty. They seem to be very well looked after."
